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Factorization Of Algebraic Expressions — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
Factorize the following expressions:$3\sqrt{3}\text{a}^3-\text{b}^3-5\sqrt{5}\text{c}^3-3\sqrt{15}\text{abc}$
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Answer

$3\sqrt{3}\text{a}^3-\text{b}^3-5\sqrt{5}\text{c}^3-3\sqrt{15}\text{abc}$$=\big(\sqrt{3}\text{a}\big)^3+(-\text{b})^3+\big(-\sqrt{5}\text{c}\big)^3-3\times\big(\sqrt{3}\text{a}\big)(-\text{b})\big(-\sqrt{5}\text{c}\big)$
$=\big(\sqrt{3}\text{a}+(-\text{b})+\big(-\sqrt{5}\text{c}\big)\big)\Big(\big(\sqrt{3}\text{a}\big)^2+(-\text{b})^2+\big(-\sqrt{5}\text{c}\big)^2\\-\sqrt{3}\text{a}(-\text{b})-(-\text{b})\big(-\sqrt{5}\text{c}\big)-\big(-\sqrt{5}\text{c}\big)\sqrt{3}\text{a}\Big)$
$=\big(\sqrt{3}\text{a}+(-\text{b})-\sqrt{5}\text{c}\big)\big(3\text{a}^2+\text{b}^2+5\text{c}^2+\sqrt{3}\text{ab}-\sqrt{5}\text{bc}+\sqrt{15}\text{ac})$
$\therefore3\sqrt{3}\text{a}^3-\text{b}^3-5\sqrt{5}\text{c}^3-3\sqrt{15}\text{abc}$
$=\big(\sqrt{3}\text{a}+(-\text{b})-\sqrt{5}\text{c}\big)\big(3\text{a}^2+\text{b}^2+5\text{c}^2+\sqrt{3}\text{ab}-\sqrt{5}\text{bc}+\sqrt{15}\text{ac})$

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